Question: $z=-24-12.7i$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=-12.7i$ and $\text{Im}(z)=-24$ (Choice B) B $\text{Re}(z)=-24$ and $\text{Im}(z)=-12.7i$ (Choice C) C $\text{Re}(z)=-12.7$ and $\text{Im}(z)=-24$ (Choice D) D $\text{Re}(z)=-24$ and $\text{Im}(z)=-12.7$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={-24}-{12.7}i$ is of the form ${a}+{b}i$, where ${a}={-24}$ and ${b}={-12.7}$. Therefore: $\text{Re}(z)={a}={-24}$. $\text{Im}(z)={b}={-12.7}$. Summary $\text{Re}(z)={-24}$ and $\text{Im}(z)={-12.7}$.